Natural Grammar
Janos J. Sarbo
Radboud University
Faculty of Science, Dept. Computer Science
Toernooiveld 1
6525 ED Nijmegen
The Netherlands
janos@cs.ru.nl
tel. +31(0)24 3653049
fax +31(0)24 3653001
Jozsef I. Farkas
Radboud University
Faculty of Science, Dept. Computer Science
Toernooiveld 1
6525 ED Nijmegen,
The Netherlands
jfarkas@sci.ru.nl
tel. +31(0)24 3653049
Auke J.J. van Breemen
Van Breemen Onderwijs Advies,
Oude Graafseweg 52
6543 PS Nijmegen
The Netherlands
abreemen@semiosis.net
tel. +31(0)24 3786910
1
NATURAL GRAMMAR
Abstract
By taking as a starting point for our research the function of language to generate meaning,
we endeavor in this chapter to derive a grammar of natural language from the more general
Peircean theory of cognition. After a short analysis of cognitive activity, we introduce a
model for sign (re)cognition and analyze it from a logical and semiotic perspective. Next, the
model is instantiated for language signs from a syntactical point of view. The proposed
representation is called natural insofar as it respects the steps the brain/mind is going through
when it is engaged in cognitive processing. A promise of this approach lies in its potential for
generating information by the computer, which the human user may directly recognize as
knowledge in a natural, hence economic way.
INTRODUCTION
What is ‘natural’ in natural language? The answer to this question evidently depends on the
interpretation of the word ‘natural’. We interpret this word as expressing that the features we
are looking for represent steps the mind or brain is going through when it is engaged in
natural language use.1 This is not to say that the representation stands for the process in all its
detail or that it describes the actual operations the brain is going through, but only that
whenever such a process occurs, that process can be represented by the steps discerned in our
model. Since this interpretation of naturalness still leaves room for different routes of
investigation we further narrow down our question to: Is it possible to develop a grammar
that captures this naturalness formally?
The promise of this chapter is that indeed it is possible to develop a natural grammar.
Additionally, our research has revealed that such a grammar is not restricted to natural
language, but can be given a naive logical and a semiotic interpretation as well. The fact that
a grammatical, a naive logical and a semiotic interpretation is possible indicates that the
corresponding different domains of knowledge can have a uniform representation, a feat that
makes our system very economic.
We maintain that an answer to ‘what is natural in language’ can be found if the function
of language as a representation of meaning is the starting point of research. According to this
view language can be seen as a kind of cognitive processing of signs. The word ‘sign’ is here
used in the broad Peircean sense according to which anything which conveys any definite
notion of an object is a sign (cf. CP 1.540).2 This embeds our original question in a more
general one: Can cognition be modeled formally as a sign recognition process? Clearly, if
such a general model can be made, then, by restricting it to linguistic signs, which are
symbols, we may obtain a natural model of language, from which an underlying grammar can
be derived easily. Since the proposed representation offers a basically computational account,
while our meaningful sign use is not confined to computation, this chapter also investigates
the complex relationship between computation and meaning.
Defining a computational, though natural representation can be difficult, as is illustrated
by traditional language modeling. Humans process natural language in ‘real-time’, which is
formally equivalent to linear complexity (Paul, 1984). This is opposed to the models of the
traditional formal approach which are typically of higher complexity. A potential side-effect
of relying on rules dictated by a formal ontology, instead of relying on the properties of a
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‘natural’ process, can be the limited expressive power of such rules for a systematic
specification of complex linguistic phenomena characterizing actual language use. We think
the natural model of language, introduced in this chapter, does not suffer from such a limited
expressive power and is on top of this efficient. While we can formally prove the last claim,
the first one remains a conjecture, in line with our assumption concerning the dynamic nature
of language. Some confidence in that conjecture, nevertheless, may be provided by the close
relationship between our model and Peirce's theory of signs and with the conclusion of
Peircean semiotic,3 which roughly comes down to the statement that ‘in order to be knowable
something has to be of the nature of a sign’.
This conclusion about the all pervasive character of signs may shed some light on natural
language and its conception as a (formal) grammar. For, by knowing the properties of the
process underlying cognition, we may be able to answer the question how ‘knowledge’, as a
cognitive process, could be defined naturally by means of (formal) rules.
Natural Grammar, as a formal grammar, bears similarity with the dependency based
formalisms of cognitive linguistics like Word Grammar (Hudson, 1984). Word Grammar is a
branch of Dependency Grammar in that it uses word-word dependencies as a determinant for
linguistic structure. As a result it presents language as a network of knowledge that links
concepts about words, like their meaning (e.g. grammatical function) to the form, the word
class, etc. Such grammars do not rely on phrasal categories. Contrary to cognitive linguistics,
which aims at incorporating the conceptual categories of language in rules which are dictated
by a formal theory, the rules of Natural Grammar are derived on the basis of an analysis of
the properties of cognition and the processing of signs. Natural Grammar is also remotely
related to constituency based approaches, in that its types of rules define an induced triadic
classification of language concepts which show some analogy to that of X-bar theory.4 The
view taken by the theories of sign processing, like the computational model of Gomes et al.
(2003) or the cognitive theory of Deacon (1997), has been a philosophical one, dominantly.
An approach, which tries to do justice to sign processing, as a cognitive as well as a semiotic
phenomenon, has been first introduced in A Logical Ontology (Farkas & Sarbo, 2000) as far
as we know. That theory forms the basis of the approach presented in this chapter.
A theory about cognition always involves assumptions about primary concepts. In the
theory presented in this chapter qualia are assumed to exist. The quale results from the
unifying operation of quale consciousness, it is upon these qualia that the intellect operates.
A quale is defined as '..every combination of sensations so far as it is really synthesized' (cf.
CP 6.223). On the one hand this leads to the conclusion that a quale is not confined to
seemingly simple sensations like in the perception of 'red', but extends to complex cases like
when we perceive a work of art, a chair or this day. On the other hand it raises the question
whether it is possible to extend our analysis in order to include the workings of our sensory
apparatus and the neuronal fabric that lead up to qualia. This later question falls without our
present scope. For the sake of completeness we mention the generative methodology due to
Pribram (1971) and Prueitt (1995), which is related to the fundamental work by Gibson
(1979). Their aim is to develop a generic mechanism for the definition of primary entities, but
also of complex process compartments, in cognitive processing. Their analysis utilizes the
concepts of measured perception and spectral properties in order to delve the gap between
mind and brain (including the sensory apparatus) or, to put it in the perspective of our model,
in order to give a physical/mental account of qualia. An analysis of the relations between that
theory and ours is beyond our scope.
TOWARDS A MODEL OF COGNITION
Cognition is concerned with the interpretation of phenomena according to their (possible)
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meaning. In this chapter we will attempt to deal with a small part of this far too complex
problem only, we focus on the restricted domain of perceptual judgments (CP 4.540).
Inasmuch as we may know about phenomena, by means of observations, the problem of sign
recognition can be reduced to a question about the nature of observations. We will consider
this issue from two points of view. The first is the cognitive theoretical one, according to
which, phenomena appear as stimuli and the question is: How can stimuli finally be
recognized in a meaningful reaction? The second is the semiotic one, according to which, we
may know about phenomena by means of signs and the question is: How can signs develop to
their meaning?
These two views are interrelated and their dependency is expressed in this chapter by
postulating that stimulus potentially is a sign, and that reaction is an interpreting proposition
by which a stimulus or percept is transformed into a fact of immediate perception. For
example, if we observe smoke, which appears as a visual stimulus or percept that can be a
sign, then shouting ‘fire!’ may be our meaningful reaction.
The problem of sign recognition gets further complicated by asking for a computational
solution, which tacitly requires a computational model for cognition that satisfies the link
between the cognitive and the semiotic viewpoints. This complication can be further
developed along two different lines.
The first line of argument is related with Searle’s thought experiment in which he
develops the Chinese Room Argument. By stating that knowledge emerges from a natural,
human process, the rules of which have to be, on that account, natural too, the following
question can be raised: Which computational rules and interpretation can satisfy this
condition in such a way that the result of the application of the rules is naturally meaningful
too? According to Searle here we are facing a fundamental problem, due to the limitations of
the computer. For, contrary to man, the computer is unable to intensionally connect a sign
with its object.
The second line of argument departs from the distinction Peirce makes between
mechanical- and purposive action. Mechanical action is characterized as a blind, compulsory
process that leaves little room for variation; just causes and effects following each other in
sequences. Purposive action on the other hand involves the mediation of a goal or purpose
that interferes with the course of events. Purposive action aims at the removal of stimulation
(cf. CP 5.563), but is quite open ended regarding the means (mechanical processes) used to
achieve this goal. It, in short, is learning and introduces abstractions by its reliance on
abductive inferences for the generation of satisfactory solutions. This kind of action may be
hard to formalize. Our current model does not capture learning, it aims at capturing habits of
thought or habits of thought like action.
COGNITION AS A PROCESS
Since we regard cognition as a process, a word about our understanding of processes is in
order at this point. A process will be considered to be any sequence of events such, that (1)
one event initiates the sequence and another terminates it, (2) every event that contributes to
the sequences yielding the terminating event is regarded as part of the process and (3) the
terminating event governs the decision of which events make up the sequence. Although the
events making up the sequence generate the terminating event (efficient causation), the whole
process is governed by its goal (teleological causation). An event will be considered as
whatever makes a difference (Debrock, Farkas and Sarbo, 1999).
The input of cognitive processing is the stimulus, which is recognized by the mind/brain.
This view of cognition is compatible with the assumption laid down by the Peircean theory of
perceptual judgments that the ‘real’ world is forced upon us in percepts (CP 2.142), from
4
which, perceptual judgments are obtained through interpretation (CP 5.54), by means of a
process which is utterly beyond our control (CP 5.115).
A fundamental property of all systems, including biological ones, is their potential for
generating an answer (re-action) to a stimulus (action). The `goal' of this process is the
generation of an adequate reaction on the stimulus, regarded as an external effect. An
important element of response generation is the interaction between the external effect
(stimulus), on the one hand, and the interpreting system, on the other. From the assumption
that the source of all reaction or meaning is an interaction and knowledge is a re-presentation
of such interactions, it follows that knowledge too must be inherently dynamic: hence a
process.
The external effect (stimulus) is affecting the interpreting system, which occurs at the
moment of affectation as a state. As anything appearing as an effect can as well appear as a
state there must be something common in both. We call this a quality, after Peirce. Because
state and effect are in principle independent, all phenomena are considered to be interactions
between independent qualities. Let us emphasize that there may be any number of qualities
involved in an interaction, but, according to the theory of this chapter, those qualities are
always distinguished by cognition in two collections (state and effect), which are treated as
single entities. The potential for considering a collection of qualities as a single entity (cf.
‘chunking’) is an assumption shared by the theory of perceptual judgments as well (CP
7.530).
Processing schema
Phenomena are an interaction appearing via the mediation of a change, as an event (cf.
reaction). Following the received theory of cognition (Harnad, 1987) the re-presentation of
phenomena by cognition can be modeled as follows.
By virtue of the appearing change, the sensory signal is sampled in a percept. In a single
operation, the brain compares the current percept with the previous one, and this enables it to
distinguish between two sorts of input qualities (in short, input): one, which was there and
remained there, which can be called a ‘state’; and another, which, though it was not there, is
there now, which can be called an ‘effect’.5 In cognitive theory, qualities as perceived are
called qualia.
The change, signifying an interaction in the ‘real’ world, can be explained as follows.
During input processing the stimulus may change, meaning that its current value and the
value stored in the last percept can be different. That difference can be interpreted by the
brain, as a change, which mediates the actual value of the stimulus to its current meaning.
The reaction of an interpreting system is determined by the system's ‘knowledge’ of the
properties of the external stimulus, including its experience with the results of earlier
response strategies (habit). Such knowledge is an expression of the system’s potential for
interpreting or combining with a type of input effect, depending on the system's state. Such
properties shall be called the ‘combinatory’ properties of the input qualia or the context of the
observation.
In complex biological systems, ‘knowledge’ is concentrated in functional units like the
sensory, central and motor sub-systems. The most important of these is the central system,
which includes the memory. The ‘translation’ from external stimuli to internal representation
(qualia) is due to the sensory sub-system, which itself is an interpreting system, generating
‘brute reactions’ (translations). For the goal of this paper, the role of the motor sub-system is
secondary, therefore omitted.
The primary task of cognitive processing is the interpretation of the external stimuli, by
making use of the latter's combinatory properties. Since the input is assumed to consist of two
types of qualia (state and effect), together appearing as a ‘primordial soup’ ([q1 q2]), the
5
stages of processing can be defined as follows (see also fig. 1). Square brackets are used to
indicate that an entity is not yet interpreted as a sign; no bracketing or the usual bracket
symbols indicate that some interpretation is already available.
(1) The sorting out of the two types of qualia in the ‘primordial soup’
as state and effect respectively.
Sorting: [q1], [q2]
(2) The separation of the collections of the two types of qualia.
Abstraction: q1, q2
(3) The linking of the qualia with their combinatory properties ([C]).
Complementation: (q1,C), (q2,C)
(4) The establishment of a relation between the completed qualia.
Predication:6 (q1,C) ─ (q2,C)
Figure 1: The schematic diagram of cognitive processing
PERCEPTION AND COGNITION
In an earlier version of the model of this paper A Peircean Ontology of Semantics (Farkas &
Sarbo, 2002) we introduced two levels of cognitive processing, which we called perception
and cognition. The ‘goal’ of perception, as a process, is the establishment of a relation
between the input qualia and the memory information (the importance of the relation between
the input qualia is secondary in this process). As a result, perception obtains the meaning of
the qualia in themselves. In accordance with perception’s goal, the memory response or the
context ([C]) contains information about the properties of the input qualia independently from
their actual relations. This information is ‘iconic’ (cf. lexical meaning).
The state and effect types of input qualia are indicated by a and b, respectively; those of
the memory by a’ and b’. All four signs may as well refer to a type as to a collection of
qualia.
Among the representations obtained by perception, only the final one (step 4) is of
interest for the rest of this paper. We assume that the a’(b’) memory response arises by means
of the a(b) input qualia, triggering the memory. Although the two types of memory response
signs are independent, they contain reference to a common meaning. This is due to the
existence of interaction between the input qualia.
Depending on the activation of the memory, there may be qualia in the memory response
([C]) having an intensity above (i) or below (ii) threshold, respectively referring to an input
(meaning) which is in the brain's focus, and which is only complementary. The distribution of
the roles in any given case depends on the actual activation of the memory which defines the
state of the mind/brain.
A high intensity response of type (i) signifies the recognition of the input as an agreement
between the input and the memory response: a(b) is recognized or ‘known’ as a’(b’). A low
intensity response of type (ii) refers to input recognition as a possibility only: the input a(b) is
6
not recognized or ‘not known’ as a’(b’) as a consequence of which the memory response only
represents a secondary or even less important aspect of the input qualia.
By indicating the first type of relationship between input and memory response by a ‘*’
symbol, and the second type by a ‘+’, the signs of perception can be represented as: a*a’,
a+a’, b*b’, b+b’. For example, a*a’ signifies the event of positive identification of a by a’
(type (i)); as opposed to a+a ' (type (ii)) which refers to the identification of a possible
meaning of a by a' (hence, to a denial of a positive identification).
In perception as an actual process the four signs are presented as a single sign. The
recognition of the difference between the four types of relations is beyond its scope.
Cognition
The process of cognition is an exact copy of the process of perception except that the ‘goal’
of cognition is the interpretation of the relation between the input qualia which are in the
focus, in the light of the qualia which are complementary. (Now it is the relation between
input and context which is secondary.) In accordance with cognition’s ‘goal’, the context
([C]) contains relational, complementary information about the input qualia, which involves
indexicality.
In the process of cognition the input appears as a ‘primordial soup’ too, which is defined
by the synonymous signs of perception. In fact, the difference between the four meaning
elements functions as a ground for the process of cognition. This is acknowledged in our
model by the introduction of an initial re-presentation of the four relations that function in
perception: a*a’ as A, a+a’ as A, b*b’ as B and b+b’ as B. The presence or absence of a
‘’ symbol in an expression indicate whether the qualia signified, are or are not in focus.
Hence ‘’ can be interpreted as a ‘relative difference’ with respect to the collection of a type
of qualia (state or effect), represented as a set. How the processing schema of sect. 4 can be
instantiated for cognition, is depicted in fig. 2.
Figure 2: The schematic diagram of cognition, as a process 7
We especially want to point to step 3, in which the link between input qualia and context
is established. This is done in accordance with the 'goal' of cognition and the duality of
phenomena alike. This explains why there can be a relation between A and B, and A and
B, and why there is no relation between A and A, or B and B.8 Finally, in step 4, the
cognition process is completed by establishing the relation between A and B.
The three relations, which correspond to the three types of interactions between the input
qualia, can be characterized by means of the meaning of their constituents (from a
computational stance this interaction is a relation that will be indicated by a ‘─’ symbol):
(1) A ─ B:
A is ‘known’, but B is ‘not known’;
7
the complementation of the input state (‘actualization’).
(2) B ─ A:
B is ‘known’, but A is ‘not known’;
the complementation of the input effect (‘refinement’).
(3) (A, B) ─ (B, A):
both A and B are ‘known’;
the assertion of the relation between A and B (‘proposition’).
If neither A nor B is `known’, interpretation terminates before reaching its goal, meaning
that cognition does not occur. The reader may have noticed the mediative function of the
context signs which is operative in step 3. Indeed, through the correspondence between the
two signs, A and B, which are triggered by the same input, the context implicitly
determines the actual relation between A and B. That relation can be called a ‘proposition’
resulting from a hypothetic inference, but only if we acknowledge, in accordance with the
Peircean view of a perceptual judgment, that the percept’s “truth consists in the fact that it is
impossible to correct it, and in the fact that it only professes one aspect of the percept” (CP
5.568).
LOGICAL ANALYSIS
The above interpretation of cognition already illustrates, to some extent, the
completeness of that process, but this becomes even more clear from a logical analysis of the
processing schema. This section is an attempt to elaborate such an analysis, on the basis of
the model of cognition introduced above. It is good to bear in mind that the results are
directly applicable to the model of perception as well. The hidden agenda of this section is
the tacit introduction of logical operations in the process model of cognition. What makes the
use of such concepts valuable is that they have a well studied, precise meaning.
An essential element of a logical approach to cognition is the abstraction of a common
meaning for the different types of qualia, which is the concept of a logical variable. In virtue
of the duality of the input, the logical interpretation of the process model of cognition
requires the introduction of two variables, which are denoted by A and B. The difference
between the qualia which are in the focus and which are only complementary, is represented
by the difference of their expression by means of a logical variable which is stated positively
or negatively. Perceived state and effect qualia which are in the focus are indicated by A and
B respectively; those which are complementary by A and B. Here, ‘’ denotes logical
negation, that is, relative difference with respect to the collection of a type of qualia,
represented as a set. For example, the complementary subsets of the set of A-type qualia are
denoted by A and A (hence the label A is used ambiguously).
Conform the above mapping, the logical meaning of the cognitive relations can be
defined in the following way. The relational operators introduced in the instantiation of the
processing schema for perception (‘+’ for possibility and ‘*’ for agreement) are inherited by
the cognitive model and its logical interpretation as logical ‘or’ (‘+’) and ‘and’ (‘*’).
[q1]= A+B, [q2]= A*B:
expresses the simultaneous presence of the input qualia which are in focus as a simple,
possible co-existence (A+B); and in the sense of agreement, as a meaningful co-occurrence
(A*B), respectively.
q1= A*B, A*B:
expresses the abstract meaning of the input qualia which are in the focus as constituents,
8
irrespective of the actually co-occurring other type of qualia. It is this perspective that
makes the two signs synonymous (the “,” in the definition of q1 directly above is a metalevel expression of this equivalence).
q2= A*B +A*B:
expresses the input as an abstract co-occurrence in terms of a compatibility relation (a
possible co-existence) of the two types of abstract constituents of the input (which are now
considered as being different). In A Logical Ontology (Farkas & Sarbo, 2000) we have
proved that the logical expression of q1 and q2 can be formally defined as the relative
difference of [q1] and [q2]. The context ([C]) is defined by the complementary qualia
represented as a co-existence (A+B) and as a co-occurrence relation (A*B). The
synonymous representation of these signs is an expression of the complementary
(secondary) meaning of the qualia, but also of the common property referred to by the
simultaneously present A and B type of qualia comprising the context.
(q1,C)= A+B, A+B:
expresses the abstract constituent (q1) completed with the meaning of the context ([C]) or,
alternatively, the ‘actual’ meaning of the input qualia as constituents. For example, the
actual meaning of A as a constituent, is defined by A itself and by B, the complementary
property linking A with B, implicitly (as the relation between A and B is not yet
established, the B type qualia cannot contribute to the actual meaning of A, as a
constituent). Alternatively, the meaning of A*B in context, is defined by the qualia
completing this abstract meaning, which are: A and B. As the two interpretations of A as
an actual constituent are related to each other by the relation of co-existence, the logical
meaning of (q1,C) can be expressed by A+B. For the same reason, as in q1, the two
representations of (q1,C) are interpreted in the model as synonymous.
(q2,C)= A*B +A*B:
expresses the abstract compatibility relation in context, thus interpreting the input as a
characteristic property which appears as an event. That such an event occurs between A
and B or, alternatively, between A and B, represents the interaction which is in the
focus, respectively, positively and negatively. Again, we refer to A Logical Ontology
(Farkas & Sarbo, 2000), in which we have proved that the logical expressions of (q1,C)
and (q2,C) can be formally defined as the logical complements of, respectively, q1 and q2,
by means of interpreting the interaction with the context ([C]) as a logical negation
operation (‘’).
(q1,C) ─ (q2,C)= A is B:
expresses the logical relation between the input qualia which are in the focus, represented
as a proposition.
The logical expressions describing the process of cognition are summarized in fig. 3. The
logical signs, ‘0’ and ‘1’, which are omitted, can be defined as representations of a ‘not-valid’
and a ‘valid’ input, respectively. Notice in fig. 3 the presence of all Boolean relations on two
variables, reinforcing our conjecture concerning the completeness of the underlying cognitive
process. The results of the above analysis show that logical signs (hence also the concepts of
cognition, as a process) can be defined as a relation (interaction) between neighboring signs
that is in need of settlement. In fig. 3, such signs are connected with a horizontal line.
9
Figure 3: The logical signs of cognition, as a process
The figure can be traversed by the application of the operation of relative difference to the
connected pairs. We make a distinction between three types of this operation. Sorting is
relative difference with respect to qualia in themselves. The input contains two types of
qualia which are in the focus, A and B, that we represent from the point of view of coexistence (A+B) and co-occurrence (A*B),9 that is to say as sorted qualia. Abstraction is
relative difference of sorted qualia with respect to each other. An example is A*B+A*B.
The reader may check this by computing (A+B)\(A*B). Complementation is relative
difference of an abstracted quality with respect to the input as a whole. An example is
A*B+A*B. The reader may check this by computing 1\(A*B+A*B).
SEMIOTIC ANALOGY
That the formal computational and the intuitive interpretation of a sign are tightly related to
each other must be clear from the above explanation of the logical relations of cognition. This
dependency forms the basis for the semiotic interpretation of those 9 types of relations, which
can be explained as follows.
[q1]: represents that the constituents are trivially part of their collection, as a whole. Hence
they are similar to it. So, the representation of the input, as a constituency relation,
expresses likeness with respect to the input, which is represented as ‘primordial soup’.
[q2]: represents that the aspect of simultaneity is a primary element of the input, as an
appearance (event) that happens now.
q1: represents that the abstract conception of the input is an expression of its being as a
qualitative possibility.
q2: represents that the compatibility of the abstract meaning of the input qualia is expressive
of a rule-like relation.
(q1,C): represents the meaning of the abstract constituents in context. It is a definition of the
actual meaning of the input qualia, as something existent.
(q2,C): represents the interpretation of the abstract compatibility relation in context as a
characteristic property; it presupposes the existence of a consensus.
(q1,C) ─ (q2,C): represents that the assertion of a relation between the input qualia involves
the formation of a proposition which is a hypothesis.
From this semiotic interpretation of the logical relations, the analogy with the Peircean
nonadic sign classification follows trivially. A serious treatment of this classification would
demand a chapter of its own; here we will have to do with some introductory remarks.10
Throughout his philosophical career Peirce was occupied with attempts to classify signs
in a systematic way. The roots of the system reside in his phenomenological work on the
Doctrine of Categories, which, in the spirit of Kant, has the task to “…unravel the tangled
skin of all that in any sense appears and wind it into distinct forms;..”(CP 1.280). This work
10
led him to believe that there are three basic categories: monadic Firstness (the possible),
which appears in consciousness as feeling or the consciousness of quality without recognition
or analysis; dyadic Secondness (the actual), which appears as a consciousness of interruption
in the field of consciousness or as the brute intrusion of another quality; triadic Thirdness (the
lawful), which synthesizes the content of consciousness or the mediation by thought of the
different feelings spread out in time (cf. CP 1.377).
The work on sign classification proceeds by repeatedly applying the three basic
categorical distinctions to signs. It starts with the definition of a sign as “…something, A,
which denotes some fact or object, B, to some interpretant thought, C.” (CP 1.346). This
definition yields three ways in which sign may be considered. First, a sign may be considered
in itself. If we do so, we neglect the relations a sign may have with its object and interpretant
and we only regard the sign as a possible sign. Second, we may regard the sign in its relation
with its object only and neglect the relation it has with its interpretant. If we do so, we regard
the sign as an existing sign, but still without any effect. And third, we may look how the sign
addresses its interpretant. If we do so, we regard the sign as a real or effectual sign. In this
last case we try to unravel the full meaning or import a sign may have by figuring out how the
sign manages to relate the interpretant of the sign with its object. If we concentrate on a signinterpretant sequence in some concrete situation, we study embedded signs.
In a second round Peirce applies the categorical distinctions to the sign relations just
discerned. The first tenable result, the nonadic classification, is summarized at the left hand
side of figure 4, the bottom right diagonal gives the relational aspects pertaining to the sign in
itself, the intermediate gives the aspects pertaining to the way the sign may relate to the
object and the top right diagonal gives the ways in which the sign may address its
interpretant. On the right hand side of figure 4 the technical terms that give the meaning
aspects are stated in more mundane terms, which are also used in the semiotic interpretation
of the 9 types of relations above.
We get at a typology of signs by selecting a term from each diagonal. The least
developed existing sign type is a rhematic, iconic sinsign (for instance a term), involving
qualisigns. The most developed an argumentative, symbolic legisign in which all less
developed signs are involved. This model of nine sign aspects yields ten sign types as a result
of the constraint that the categorical value of a term on a higher right diagonal cannot be
higher then the value of a term on a lower right diagonal. By taking the process of cognition,
which always is an argument, as our focus and by assuming that all less developed meaning
aspects are involved, we turn the static nonadic classification into a dynamical process model.
Figure 4: The Peircean types of signs and their aspects of meaning
It is important to note that we interpret the relational aspects of the nonadic classification
as the parameters of (full) meaning. The isomorphism between the cognitive process and
Peirce's nonadic classification is a consequence of the isomorphism between the induced
order of cognitive processing, on the one hand, and the interdependency of the Peircean sign
aspects, based on categorical distinctions, on the other. But this is all there is! The model
introduced in this paper is suited for a computational interpretation. But, although the above
mapping establishes a link between the Peircean signs and the Boolean logical relations,
hence define a computational level of authentic semiosis, the full meaning of the Peircean
sign types is qualitatively more than such logical relations, since the relations always exist
11
between two sign aspects, while a sign type irreducibly contains three aspects. Finally, let us
mention that the process view of signs can be introduced also from the Peircean theory itself
(see Debrock, Farkas & Sarbo, 1999).
By assuming that the full meaning of a sign emerges, through embedding in real life
interaction with the world, from the relations ‘generated’ by cognitive processing, the 9 sign
aspects can be hypothetically considered to be a link between the computational and the
semiotic level of meaning. Inasmuch as those aspects are enclosed in a process, which finally
results in something that can be characterized as truly meaningful, it is probably best to
consider the 9 aspects as unfinished ‘meaning elements’, that is, as signs which are in a
process of becoming signs (Breemen & Sarbo, 2005). Such signs are called in this paper, preor proto-signs11 (Sarbo, 2005).
The different characterizations of knowledge - a combinatory process of qualia (fig. 2); a
representation of logical relations (fig. 3); a hierarchy of increasingly more complex
‘meaning elements’ (fig. 4); but also its other possible interpretations - are interrelated, and it
is their collection that approaches full meaning. The conjecture of this research is that, if a
uniform representation can be proved to exist, this can be the key for an efficient
(computational) merging of knowledge obtained in different domains, into a single
representation. Experimental evidence pointing in this direction is found in Hagoort et al.
(2004).
COMBINATORY RELATIONS AND PROPERTIES
We may observe an entity, as a state, only by virtue of an appearing effect, but the occurrence
of an effect always entails the existence of a state. This asymmetry between state and effect is
the ground for a semiotic interpretation of the differences between the three types of relations
recognized by cognitive processing.
(1) A ─ B:
A is a potential meaning, which is actualized by B.
(2) B ─ A:
B, which is in principle self-sufficient, receives its
full meaning from its association with A.
(3) (A,B) ─ (B,A):
A and B, which are self-sufficient both,
together generate a new meaning.12
The interpretation of these (cognitive) relations, as syntactic signs, has been introduced in
Syntax from a Peircean perspective (Debrock, Farkas & Sarbo 1999). Syntactic signs, which
are a representation of the three types of a nexus between syntactic symbols, correspond to
the Peircean categories of Firstness, Secondness and Thirdness, for example, a primary
syntactic entity (a word), a syntactic modification (of a noun by an adjective) and syntactic
predication (subject and predicate forming a sentence) respectively. The important
consequence of this transitive relation between cognition and the categories is the existence
of a necessary and sufficient condition for ontological specifications, which are typically
syntactic relational too, in particular those which are also meant to be used in computer
applications. The analysis of the meaning of the constituents, in the three types of relations,
proves that the specification of the (combinatory) properties of qualia can be restricted to
three cases. The specification of
(1) the qualia in themselves;
(2) with respect to other qualia which are complementing it
12
or, which they are complementing;
(3) with respect to other qualia, together with which, they can
generate a new meaning.13
We call such a specification a trichotomic specification or, briefly, a trichotomy. In virtue
of the dependency between the Peircean categories, the meaning of a more developed class
contains the meaning of a less developed one, in a trichotomy. By assuming that the three
types of meanings can be defined in each trichotomic class, recursively, we have in front of
us the hierarchical schema of ontological specification suggested by the theory of this
research.
A framework which is remotely related to the approach presented here, is the theory of
Nonagons (Guerri, 2000), which has been introduced originally for supporting the
completeness of a design, for example, an architectural design. Nonagons are also based on
Peirce's sign aspects and a recursive expansion of his nonadic classification. There is
however an important difference between the two approaches in regard to the interpretation
of a sign, either as an entity which emphasizes its character as a single unit (the Nonagon
approach) or, as an entity which stresses the inherent duality implied by truly triadic
semeiosis (the view maintained by this work).14 A practical advantage of the latter view lies
in its capacity for defining the 9 classes as a product of (dual) trichotomies, thereby
simplifying the specification task, potentially. An example, illustrating the benefits of
recursive specification of the properties of qualia, in text summarization, is presented in
(Farkas & Sarbo, 2005) and (Sarbo & Farkas, 2004).
In sum, there are 3 types of relations between signs, in accordance with the 3 categories
of phenomena. Qualia, which are the constituents of a syntactic sign interaction, can be
analogously characterized, recursively as:
(1) a quality, which is a potential existence;
(2) a state, which appears by virtue of an effect (a or A);
(3) an effect, which implicates the existence of a state (b or B).
The three categories are not independent from each other. Though thirdness is the most
developed, nevertheless it requires secondness and firstness (the latter via the mediation of
secondness). Analogous with the categorical relations, an effect can be said to contain a state
and, transitively so, a potential existence. By means of the induced ordering of the
dependency between the categories (‘<’), as a polymorphic operation, the relation between
the cognitive types can be abstracted as follows: a<b and A<B. For example, the meaning of
a quale which is an effect, implies the existence of its meaning as a state.
Example
This section contains an example, illustrating the recognition of the ‘real’ world phenomenon,
smoke, as the sign of danger. Assume, we are watching for some time the smoke rising from
the chimney of a roof, and suddenly we ‘see’ fire to blaze up. The input qualia of perception
can be defined as follows (boldface symbols are used to indicate input qualia):
a= smoke, b= fire
and the final signs of perception, re-presented as the initial signs of cognition (italic is used to
indicate memory signs):
13
A= smoke*smoke,
B= fire*fire,
A= smoke+roof-in-burning
B= fire+burning
The recognition of these signs yields the following relations (in a reference to an
interpretation which is dealt with as ‘not known’, the input is omitted):
(q1,C)= (smoke*smoke, burning)
(q2,C)= (fire*fire, roof-in-burning)
which together generate the proposition, through the mediation of the burning of the roof:
(q1,C) ─ (q2,C)= (smoke
) IS (fire
)
This sign can be re-presented, eventually, by shouting “Fire!” or, simply, by “running away”,
as our interpretant reaction, assuming there is a real need.
In order to enable the recognition of the input as such a meaningful relation, the input
qualia have to be adequately specified by means of trichotomies. Let us exemplify this with
the specification of smoke (hence implicitly also of smoke), which can be regarded:
(1) in itself: as an entity which is a quale, having properties underlying its combinatory
potential, like color, density, etc.
(2) in relation to another quale which is complementing it: e.g. rising-from-the-chimney; or,
which it is complementing: e.g. blowing (as a smoke producing effect).
(3)as a self sufficient sign: like the subject of any-burning.
Notice that the qualia of (1) function as the ground for the connections of (2), which in turn
underlie the meaningful relations of (3).
NATURAL LANGUAGE
The process model of cognition can be applied to natural language easily. In natural language
the input qualia can be a morpheme or a word (a morpho-syntactically finished symbol), in a
morphological and a syntactical analysis, respectively. The perception process, linking the
input with memory information, corresponds to lexical analysis. The ‘single stimulus’ or
percept view of the cognitive model of this chapter requires that, conceptually, the entire
input is present in a single observation. To this end, the order of appearence of the input
symbols can be represented as a quale,15 which eventually leads to a sequential model of
cognitive processing. In the model of language, as syntactic signs, the second process
(‘cognition’) corresponds to parsing, interpreting the input symbols, as (morpho-)syntactic
relational needs (combinatory properties), which may combine (bind). In the rest of this
chapter the focus will be on syntactic symbols, the process of morpho-syntactic recognition is
omitted.
Step 1 (cf. fig. 1) corresponds to the classification of the input symbols as nominals ([q1])
and non-nominals ([q2]). Which one of the symbols is in the focus, and which is only
complementary, follows from the syntactic rules and the order of appearance of the input
symbols. Step 2 amounts to the identification of noun (q1) and verb phrases (q2) but also of
modifiers and complements ([C]), step 3 is devoted to modification ((q1,C)) and
complementation ((q2,C)), and step 4 to syntactic predication.
The classification of syntactic concepts is depicted in fig. 5, on the left-hand side. On the
14
right-hand side you may find an illustration of the syntactic concepts, by the analysis of a
simple utterance. The goal of this example is twofold. The first is an analysis of syntactically
meaningful concepts and their dependency; the second is an illustration of the sequential
order of the input symbols (cf. surface structure) as potentially meaningful.
Figure 5: The classification of syntactic concepts and the concepts of the sample utterance `John likes Mary'
Sequential processing
Contrary to the earlier example of smoke-and-fire, in the language phenomenon presented in
fig. 5, “John likes Mary” (in short J l M), we have more than two qualia, but these too can be
distinguished in two collections: [JM] and [l]. These collections are interrelated: ‘[l] happens
to [JM]’. The linguistic interpretation is more refined, however. The relation between l and J
is different from the one between l and M. This difference is signified, in English, by means
of the order of the input symbols. This ordering, as a quale, is recognized by the language
user, together with the other meaning(s) of the involved symbols.
This line of thinking has led us to a sequential version of our model of language, in which
the effect of the order of the input symbols is defined by means of the nine Peircean sign
aspects (Sarbo & Farkas, 2001). On surface level, the input symbols appear one after the
other. Because each symbol may contribute to the meaning of the entire sequence (the
sentence) only as a proto-sign, the recognition of the individual input entities may overlap. In
general, the processing of subsequent sentences may overlap as well. In the utterance of
fig. 5, the input symbols appear as qualisigns.16 As the input qualia are, in principle,
independent, but also partake in the same sentence (phenomenon), the appearance of l forces
us to reconsider the earlier interpretation of J (qualisign). A possible solution of this can be
the re-presentation of J, as a constituent (icon) of the entire input, in accordance with the
principle of economy, characterizing language recognition, which states that a less developed
representation of a phenomenon has to be generated before a more developed one.
The appearance of M has similar consequences on l and, transitively so, on J. The latter is
due to our assumption that the signs yielded by ‘sorting’ (cf. sect. 4) signify the qualia of a
single phenomenon, as potential co-existence (icon) and co-occurence (sinsign). As J and l
together do not mediate such a meaning, it follows that J has to be re-presented again, but this
time as a possible abstraction of the entire input (rheme). Notice that any re-presentation of a
symbol must contain the earlier meaning states of the same symbol. The subsequently
appearing dot symbols (the role of which will be explained in the next section) trigger a chain
of representations, of which we explain only the re-presentation of the nominal meaning of M
(icon). We start with applying the same strategy, like in the case of J (icon), but then parsing
will eventually fail, as we cannot represent the entire input in a single sign. So, we assume the
parser backtracks until the first point that provides an alternative17 which represents M as a
complement of l. This example also illustrates how our model may discover whether a
symbol is part of the complementary context, if that property is not indicated otherwise. The
parsing of the example of fig. 5 is displayed in fig. 6.
15
Figure 6: Syntactic analysis of ‘John likes Mary’
Due to the sequential processing of the input we have to consider two new cases of an
interaction (relation) between symbols: the first is accumulation, which is a ‘binding’
between signs having an identical status and compatible information; the second is coercion,
which is an interaction that does not actually happen. What does happen in such an
interaction is that an existing sign is forced to be re-presented by or is ‘coerced to’ a more
meaningful interpretation. Coercion and accumulation are degenerate versions of (normal)
binding.
The specification of the qualia with respect to other qualia which are complementing it
or, which they are complementing (cf. sect. ‘Combinatory relations …’), corresponds to
syntactic modification and complementation, respectively. This indicates that the two types
of phenomena can be treated uniformly, in our model.
Towards a formal model
The syntactic interpretation of the classification of qualia (cf. sect. ‘Combinatory relations
…’), as the constituents of a binding defines the three types of syntactic relational needs
acknowledged by our model: (1) neutral, (2) passive and (3) active (in short, n-, p- and aneed). The ‘goal’ of language cognition, as a syntactic process, is syntactic well-formedness.
This is formally interpreted by requiring that the final representation of the (entire) input may
not have any unsatisfied relational needs; it must be neutral, syntactically. The different types
of binding can be characterized, from this point of view, as follows. A coercion ‘satisfies’ an
n-need; in an accumulation two relational needs of the same type are merged to a single need;
a (normal) binding satisfies a pair of a- and p-needs.
Fig. 7 summarizes the potential syntactic relational needs for the types of speech. The
input qualia are defined as follows: A=noun; B=verb, adjective, adverb,18 prep(-compl),
where ‘compl’ can be a noun, verb, adjective or adverb. The trichotomic specification of
syntactic symbols is such that, through re-presentation, A-type symbols can have a relational
potential, as an (1) icon, (2) rheme or index, and (3) a dicent type of sign; and, B-type
symbols, as a (1) sinsign, (2) legisign or index, and (3) a symbol type of sign. In English, the
category related dependency between the different interpretations of a symbol, as an A- or a
B-type quale, is used, amongst others, for the modeling of modification phenomena like
‘runs quickly’. In this example, the a-need of quickly (index) satisfies the p-need of runs
(legisign), indicating that the effect (run) is considered in this interaction, as a state (run).
Also, object complementation phenomena like ‘painted black’ can be modeled
isomorphically.
We define a ‘dot’ symbol as an A and B type sign, which cannot bind except with its own
type. Dot symbols can be used to force the ‘realization’ of pending interactions. We assume
that the entire input is closed by a constant number of dots. From the specification of fig. 7
and the earlier introduced properties of sequential processing, a formal definition of a Natural
16
Grammar of English can be derived easily19 (Sarbo & Farkas, 2002). In figure 7 optional nneeds are omitted.
Figure 7: Classification of syntactic symbols
The kernel of an algorithm for the parsing of coordination has been presented in (Sarbo
& Farkas, 2004). The essential point of this algorithm is the merging of signs having an
identical sign type, to a synonymous meaning. Multiple modification and complementation,
but also embedded clauses can be modeled by means of recursive incarnations of the parsing
‘machinery’. In (Sarbo & Farkas, 2002) we formally proved that the complexity of cognitive
processing in our model is linear in the number of input qualia, and operations on them.
Example
This section is an attempt to illustrate the potential of our approach for modeling complex
linguistic phenomena. The presentation of the analysis is simplified by introducing a tabular
form for the sign ‘matrix’ as used in fig. 6, in which, a column corresponds to a sign aspect,
used as an indicator of the processing status, and a row to re-presentation act(s), arising due
to the application of rules, indicated in last column. The following abbreviations are used:
input (i), accumulation (a), coercion (c), binding (b). Accumulated signs are separated by a
“/” sign. The names of some of the sign aspects are abbreviated. The parsing of dot symbols
is omitted. Predication is not displayed due to lack of space.
Table 1: Syntactic analysis of A man entered who was covered with mud
nr.
0
1
2
3
4
5
6
7
8
qual
a man (am)
entered(e)
who(wh)
recursion
was covered (wcd)
with mud (wm)
return
9 who-..-mud(wcm)
10
11
12
13
icon sins rhem index legis dicent
symbol
i
i,c
i,c,c
am
e
am
wh
wcd
wm
e
wcm
wh
wh
wh
am
am
am
rule
wm
wm
wcm
wcd
wcd
wcd
e
e
e
wh
wh
ahm-wcm
am-wcm
wcd-wm
i,c
i,c,c
c, c
c
c
b
e
i
c,c
c
b
c
The first example illustrates discontinuous modification. Let us take as our starting point
the morpho-syntactic analysis of the sample utterance: (A man) (entered) (who) (was
17
covered) (with mud). In the syntactic parsing (cf. table 1) we make use of recursion in the
analysis of the segment initiated by ‘who’ and closed by the sentence ending dot. In the
recursively analyzed part, ‘who’ functions as a (dummy) subject. The final sign of this
segment is represented degenerately, by a single quale (wcm), having an adjective-like
relational need due to the unsatisfied relational need of ‘who’.
The second example (cf. table 2) illustrates coordination. We assume the morphosyntactic analysis: (Mary) (is) (a democrat) (and) (proud) (of it). In the syntactic analysis, in
step 8, ‘proud’ and ‘of it’, are accumulated in a single sign. The coordination of ‘proud of it’
with ‘a democrat’ is possible, as both symbols can be ‘is’-complements, syntactically.
Table 2: Syntactic analysis of Mary is a democrat and proud of it
nr.
0
1
2
3
4
5
6
7
8
qual
icon sins
Mary(M)
is(i)
M
a democrat (ad)
and(&)
ad
i
rhem
index
M
M
ad
save
proud(p)
of it(oi)
p
oi
legis dicent
i
i
symbol
rule
i
i,c
i,c,c
i,c,c
c,c
M
i
i,c
c,c
c,a
p
p/oi
coordination
9
ad&p/oi
restore
10
11
ad&p/oi
i
M
M
i-ad&p/oi
b
SUMMARY
An advantage of our model of knowledge representation presented in this chapter lies in its
potential for generating information by the computer, that the human user may directly
process naturally. The essence of such processing can be explained by means of the metaphor
of apparent motion perception. If the snapshots of a series are presented correctly, we may
easily experience the meaning of the series, as a whole. If the presentation is not correct, as
for example when the snapshots are in the wrong order or the difference between the
consecutive pictures is too large, an adequate interpretation may still be possible, but it can be
difficult.
The idea behind our theory is that an analogous “correct” presentation of information in
knowledge modelling, may entail an immediate ‘natural’ interpretation of the computations
yielded by the cognitive model (cf. frames), as different representations of a single interaction
between some state and effect. More specifically, the hypothesis of this work is that
information processing that does respect the 9 types of relations of cognitive processing and
their ordering, may enhance the interpretation of the full meaning of such computations as a
whole (through the mediation of proto-signs).
This relation between the cognitive and semiotic concepts of meaning production is the
key to the natural definition of the combinatory properties of qualia in language as a habit.
Additionally, the processual interpretation of the Peircean classification is the key to the
understanding of sign recognition, generating increasingly better approximations of the final
meaning of the observed phenomenon. It can be shown that there exists a correspondence
18
between the types of relations generated by cognitive processing on the one hand, and the
interactions between sign aspects that are each other's neighbors,20 according to Peirce's
classification, on the other. From the isomorphism of the representation of knowledge in
different domains it follows that different interpretational viewpoints (like syntactic, logical,
etc.) can be merged to a single whole through coordination (in a broad sense).
What is `natural' in natural language? In our view the natural aspect of language involves
the types of distinctions that can be made cognitively; the organization of such events in a
process; and the appearance or ‘feeling’ of such a process as knowledge (the last lies beyond
the scope of our model). This is the basis, in our opinion, for the understanding of
computational semiotics as a cognitively based semiotic and, therefore, as natural
computation.
19
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1
We acknowledge that a distinction can be made between natural and designed languages like Esperanto. The
origin of the language however is of no consequence for our present concerns.
2 A reference to Peirce (1931) is given by volume and paragraph, separated by a point.
3 Peircean scholars also use the term semeiotic.
4 The three concepts of X-bar theory, which are denoted by X, X' and X", are a representation of a lexical
category, a relation and a phrase, respectively.
5 The importance of similarity (comparison) in cognitive theory is also emphasized by Goldstone & Barsalou,
(1998).
6 This whole process is beyond our direct conscious control.
7 Here and in later diagrams a ‘’ is denoted by a ‘~’ symbol.
8 A and A (but also B and B) arise due to the same input trigger, indicating that the two signs are not
independent.
9 As A and B are commonly considered as logical variables, the separate representation of the input qualia
contains both variables. The difference between their meaning as co-existent and co-occurrent is expressed by
means of the ‘+’ and ‘*’ operators respectively.
10 For a detailed treatment see Liszka 1996.
11 We gladly acknowledge that the term proto-sign has been suggested by Gary Richmond.
12 Conform our assumption that all interaction is between state and effect, the constituents of a type (3) relation
show an analogous difference.
13 Notice that (1) allows only a single interpretation, (2) provides two and (3) can be expanded in three
meanings, that differ from each other in the question which one of the qualia has a dominant function in the
relation (either the one, or the other, or both).
14 Both models depart from a triadic definition of signs, but the difference in goals served puts a different
emphasis on the properties of signs. We maintain that full understanding of semiosis is only possible when the
different perspectives are combined.
15 Cf. the phenomenon of embedding in sect. ‘Towards a formal model’.
16 Please note that in this analysis the Peircean terms are used as pointers to the status of a language symbol in
the process of parsing.
17 We assume non-determinism is implemented by backtracking.
18 In virtue of the sequential character of language processing, also adjectives, adverbs, etc. are considered as
appearing effects and treated as B-type qualia.
19 Essentially such a grammar consists of rules, which are instances of the syntactic relations - sorting,
abstraction, complementation and predication - as rule schemas. Schema instantiation is lexically driven by the
defined combinatory properties of the syntactic qualia.
20 The neighborhood relation is indicated by horizontal lines in fig. 3, sect. ‘Logical analysis’.
21